AD-GBC: Anisotropic Granular-Ball Skip-Connection Refiner for UNet-Based Medical Image Segmentation

Prototype or region-attention modules have recently improved medical image segmentation but still suffer from two fundamental limitations: 1) they represent each semantic concept as a point or isotropic region, failing to capture the inherently anisotropic geometry of real feature distributions; and 2) many rely on non-differentiable clustering or one-way kernel weighting, which restricts their ability to form coherent region-level representations. We address these issues with the Anisotropic Differentiable Granular-Ball (AD-GBC) module, which generalizes prototypes into learnable geometric regions parameterized by a center and an anisotropic vector scale. AD-GBC aggregates local features into region-level semantics and redistributes the refined representation back to pixels in a fully differentiable manner, enabling geometry-aware refinement within modern UNet-style architectures. Two geometric regularizers, a Wasserstein-based diversity loss and a scale consistency loss, mitigate center collapse and encourage stable, wellformed region geometry. AD-GBC yields consistent improvements across four widely used medical segmentation benchmarks (BUSI, GlaS, CVC-ClinicDB, ISIC17) when integrated into two strong backbones (Rolling-UNet and U-KAN), demonstrating that the proposed geometric region formulation generalizes well across different imaging conditions. The code is available at https://github. com/SiaShen-dot/AD-GBC.